The current information-oriented society is supported by semiconductor devices represented by CMOS (complementary metal oxide semiconductors) based on silicon. The silicon semiconductor industry has heretofore achieved miniaturization with both of high integration and high performance by continuously decreasing applicable ranges of microfabrication technology, such as lithography technology, etching technology, and deposition technology, from micrometers to several tens of nanometers. However, it is inevitable that the device dimension will reach an atomic level or a molecular level in the near future. Thus, there have been pointed out physical limitations of conventional semiconductor materials such as silicon and device structures.
In order to breakthrough such an obstructed situation, novel semiconductor materials and device structures based on a new concept are being sought at the present time. Graphene, which has attracted much attention in recent years, may have great potential to meet those demands.
Graphene is obtained by separating only one layer of graphite, which is a layered material formed of only sp2-hybridized carbons. Graphene is a stable monatomic-layer planar material.
Generally, graphene refers to one layer of graphite. Nevertheless, graphene may refer to two or more layers of graphite in some cases. Graphene has a structure of a quasi-two-dimensional sheet in which six-membered carbocyclic rings, each of which has a regular hexagonal shape with carbon atoms at its vertexes, are closely packed in a honeycomb lattice. The distance between carbon atoms is about 1.42 Å (angstroms) (=0.142 nm). In a case where a substrate is formed of graphite, the thickness of the layer is 3.3 Å to 3.4 Å (=0.33 nm to 0.34 nm). In cases of other substrates, the thickness of the layer is about 10 Å (=1.0 nm). The graphene plane can be assumed to have various sizes ranging from a molecular size in which the length of a piece is on the order of nanometers, theoretically, to an infinite. Furthermore, graphene has a three-fold rotoreflection axis on the plane, which results from its honeycomb structure. Therefore, when graphene is rotated around a certain point through 120 degrees on the plane, it coincides with the original structure.
Graphene has two characteristic edge structures, one of which is an armchair edge, the other of which is a zigzag edge. Since a graphene plane is of three-fold rotoreflection, the armchair directions and the zigzag directions respectively appear with every 120-degree rotation on the plane. The armchair directions and the zigzag directions are perpendicular to each other.
According to the preceding research, a phenomenon has been observed in which those two edge structures are produced when a graphene is torn by an external force. The cause for this phenomenon is the fact that a graphene tends to shear in its armchair directions and zigzag directions. For example, Nature, Vol. 367, 148-151, 1994 (Non-patent Document 1) and Advanced Materials, Vol. 7, No. 6, 582-586, 1995 (Non-patent Document 2) illustrate a graphene having a regular geometric structure, which remains on a surface of graphite after the graphite has been peeled off. Japanese Patent No. 2541091 (pp. 6-8; FIGS. 3-10) (Patent Document 1), which corresponds to U.S. Pat. No. 5,925,465 (Jul. 20, 1999), Sheets 2 to 8, FIGS. 3 to 8, discloses a method of manufacturing a graphene on the order of submicrometers with use of an atomic force microscope (AFM). Furthermore, with a scanning tunneling microscope (STM), a phenomenon has been observed in which the two characteristic edge structures of an armchair edge and a zigzag edge are produced when a graphene is heated on a surface of graphite. This phenomenon relates to the roughening transition and occurs conceivably because the armchair edges and the zigzag edges are more stable in thermodynamics than other edge structures.
For example, Journal of Materials Research, Vol. 16, No. 5, 1287-1292, 2001 (Non-patent Document 3) describes the details of holes having a geometric shape of submicrometers with a characteristic edge structure provided by heating a graphene. Japanese patent No. 3447492 (column 7, line 43 to column 10, line 30; FIGS. 3-11) (Patent Document 2), which corresponds to U.S. Pat. No. 6,540,972 B1 (Apr. 1, 2003), column 5, line 16 to column 9, line 19, FIGS. 3-11, discloses a method of forming a graphene piece having a geometric shape by systematically arranging those holes.
As described later, if a graphene has a size of the order of nanometers, the quantum size effect becomes so significant that an edge structure of the graphene, such as an armchair edge or a zigzag edge, defines electronic properties of the graphene.
According to the recent research, the field effect in a semimetal graphene has been reported in Science, 306, 666-669, 2004 (Non-patent Document 4). In a device using a metal graphene shown in Non-patent Document 4, a metal graphene piece, which serves as a channel, is disposed on a highly-doped silicon substrate via a silicon oxide. Both ends of the metal graphene piece are connected to two gold electrodes so as to form source and drain electrodes. Thus, a field-effect transistor is formed with highly-doped silicon serving as a back gate electrode. A metal graphene piece is obtained by using standard lithography and etching to cut graphene out of a surface of highly-oriented pyrolytic graphite (HOPG). Because the graphene channel of this device has a large width of at least 80 nanometers, it exhibits no quantum size effect resulting from its edge structure, i.e., it is fundamentally metallic. Generally speaking, the field effect can be observed only in semiconductors, but not in metals because the electric field is allowed to penetrate deeply into semiconductors, but never into metals. Nevertheless, the field effect is seen in a metal grapheme. The reason for the extraordinary phenomenon is because the metal graphene used has only one to several layers and is thus extremely thin in the thickness direction such that an electric field due to a gate electrode can surpass the shield due to carriers in the graphene channel. Since the graphene channel is not intentionally doped, the same number of conduction electrons and positive holes are present for carriers when a gate voltage is zero without an electric field. If a negative gate voltage is applied, electrons are depleted such that positive holes are increased and thus used for conduction. If a positive gate voltage is applied, positive holes are depleted such that electrons are increased and thus used for conduction. In other words, while this device demonstrates what is called ambipolar conduction, both of electrons and positive holes cannot be depleted simultaneously. Thus, the device does not completely establish an off state. Therefore, in view of standard performance characteristics of a field-effect transistor, this graphene device exhibits low performance. However, this device has attracted much attention as a very interesting material in pure physics because a metal graphene behaves as a two-dimensional gas that is ideal and unique. Some reports on use of a metal graphene device having substantially the same configuration as that in Non-patent Document 4 are included in Nature, 428, 197-200, 2005 (Non-patent Document 5) and Nature, 428, 201-204, 2005 (Non-patent Document 6). Non-patent Documents 5 and 6 have reported relativistic quantum mechanical effects that have not ever been measured, such as massless electrons and the unusual integer quantum Hall effect, which has not been seen in general metals, and have thus made great contributions to enhancement of human intelligence and development of science.
Additionally, Science, 312, 1191-1196, 2006 (Non-patent Document 7) has reported technology of producing a graphene on a silicon carbide (SiC) substrate with illustration of a prototype of a graphene device in which all of source, drain, and gate electrodes are formed of graphene. However, in the graphene device shown in this document, the edge structure of the graphene channel is not controlled. In the first place, the width of the graphene channel is about 100 nm, which is too large to exhibit the quantum size effect.